Ray Optics and Optical Instruments · Question 59

A hemispherical vessel is completely filled with a liquid of refractive index . A small coin is kept at the lowest point (O) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is . [figure]

1. 32
2. 32
3. 3
4. 2

Answer

(4) 2

Solution

To reach E (at the level of the surface), the ray from O must emerge grazing the surface at B, i.e. angle of refraction = 90 .

[figure]

Ray OB: O is at depth R below C and B is at distance R from C

OB makes 45 with the vertical CO; the normal at B is also vertical, so the angle of incidence at B is i = 45

Snell's law at B: 45 = 1 90

= 2 (minimum value; any smaller μ cannot bend the ray to E)

Answer: (4)